Fewer studies have examined the effects of source-specific particle
contributions or individual particle species. Several large multicity
studies have reported stronger associations for particle sulfate and
nickel (Bell et al. 2014; Dai et al. 2014; Franklin et al. 2008). The
U.S. Environmental Protection Agency's (EPA's) recent
transport regulation has already produced substantial reductions in
sulfate particles, and is scheduled to reduce remaining sulfur emissions
further in the next few years (U.S. EPA 2016). As the sulfate
contribution to particle mass declines and NOx (nitrogen oxides)
controls affect secondary organic particle formation, local emissions of
particulate and gaseous pollutants will become a more important part of
the pollution mix; thus it is important to enhance our understanding of
their health impact.

There are fewer and less consistent studies assessing the effects
of particle components. For example, Krall et al. (2013) and Bell et al.
(2014) reported a greater toxicity for elemental (or black) carbon, a
large fraction of which is associated with local traffic and domestic
heating, whereas Franklin et al. (2008), Beelen et al. (2015) and Dai et
al. (2014) found greater effects for sulfur and not elemental carbon.

There is biological support for a role of local traffic particles.
Diesel particles have been shown to increase oxidative stress in
endothelial cells (Furuyama et al. 2006; Hirano et al. 2003), inducing
the production of heme oxygenase-1, a rapid response part of the
body's defense system against oxidative stress (Choi and Alam
1996). The viability of cell cultures of microvascular endothelial cells
was also impaired by diesel particles with an accompanying large
increase in induction of heme oxygenase-1 (Hirano et al. 2003).

A key gap in the analysis of the acute effects of local air
pollution sources has been the lack of studies done in the framework of
causal modeling, specifying potential outcomes, and basing their
analysis on estimating the difference or ratio of potential outcomes
under different exposures. In this paper, we use a causal modeling
framework to estimate the causal acute effects of local pollution on
daily deaths.

Methods

Causal Modeling

To establish causality specification of potential outcomes is
required. We designate [Y.sup.A=a.sub.i] as the outcome that would occur
given an exposure A = a for the unit i, and [Y.sup.A=a'.sub.i] to
be the outcome that would occur if the unit i were instead exposed to an
alternative exposure, A = a'. Causal modeling seeks to estimate the
ratio of the expected value of outcome in the population of subjects i
under the exposure they received versus what it would have been had they
received the alternative exposure:
E([Y.sup.A=a.sub.i])IE([Y.sup.A=a'.sub.i]). Because only one
potential outcome is observed, various methods seek legitimate
surrogates for the unobserved potential outcome (Hernan et al. 2008). In
this paper, we apply the approach of instrumental variables. An
instrumental variable is a variable that is related to outcome only
through the exposure of interest.

Instrumental Variables

Let [Y.sup.A=a.sub.t] be the potential outcome (total deaths) in
the population of a city exposed to A = a on day t, and let
[Y.sup.A=a'.sub.t] be the potential outcome under the alternative
exposure a'. We would like to estimate
E([Y.sup.A=a.sub.t])IE([Y.sup.A=a'.sub.t]), but only
[Y.sup.A=a.sub.t] is observed. We assume the potential outcome depends
on predictors as follows:

where [Y.sup.A=a.sub.t] represents the potential outcome at time t
under exposure a, [[theta].sub.0] and [[theta].sub.1] are the intercept
and the slope of exposure, respectively, and [[PHI].sub.t] represents
all of the other predictors of outcome. Unless we have measured all of
the confounders, standard methods, including standard approaches to
causal modeling, will give biased estimates of [[theta].sub.1]. However,
air pollution has many sources of variation. If there is a variable Z
that is one such source of variation in exposure, and Z is associated
with Y only through A, then Z is called an instrumental variable. Figure
1 shows the directed acyclic graph (DAG) for this scenario.
Consequently, [A.sub.t] can be expressed as follows:

[A.sub.t] = [Z.sub.t][delta] + [[eta].sub.t], [2]

where nt represents the other sources of variation in exposure, and
particularly all of the exposure variations that are associated with
other measured or unmeasured predictors of outcome. This follows because
of the instrument assumption, that Z is only related to Y through A.
Formally, E([Z.sub.t][[PHI].sub.t]) = 0 because of the instrument
assumption. Then let Z1 and Z2 be equal to Z such that:

As a result, if we use Z as an instrument for A, we can recover a
causal estimate for [theta], which is the log rate ratio. Importantly,
this is true even if there are unmeasured confounders.

Put less formally, in an observational study the exposure is not
randomly assigned, so it may be correlated with other predictors of the
outcome. However, air pollution (and other exposures) varies for many
reasons. Some of them may be correlated with other predictors of daily
deaths. For example, worse-than-average traffic on 1 day will increase
both air pollution and stress. However, some sources of variation in air
pollution may not be correlated with other predictors of daily deaths.
For example, wind speed is unlikely to be correlated with daily stress,
smoking, and the like. Hence, if this is true, the fraction of air
pollution variation that is produced by wind speed is randomized with
respect to confounders, including unmeasured ones; and if that fraction
is associated with daily deaths, the estimated effect should be causal.
We discuss this further below.

Planetary Boundary Layer and Wind Speed as Instruments

The difficulty with instrumental variable analyses is finding a
valid instrument that is associated only with outcome through the
exposure of interest. Mendelian randomization is an example of an
instrumental variable successfully applied in epidemiology, and is
justified by knowledge that the biological pathway by which the genotype
is associated with exposure is not associated with other predictors of
outcome (Holmes et al. 2014). Hence external knowledge is critical to
the technique.

The air pollution above a city is a mix of locally emitted
pollutants and pollutants transported from elsewhere. The lowest part of
the atmosphere, along with its behavior, is influenced by its contact
with a planetary surface, which is called planetary boundary layer (PBL)
and is characterized by strong vertical mixing (Finlayson-Pitts and
Pitts 1986). Above the PBL lies the free atmosphere, which is mostly
nonturbulent. The transport of pollutants from the boundary layer to the
free atmosphere is slow relative to their vertical mixing within the
boundary layer (Seinfeld and Pandis 1998). Therefore, the impact of
local emissions on pollutant levels is directly related to the height of
the PBL (e.g., for the same local emissions, concentrations of locally
emitted pollutants are higher when the boundary layer is low and vice
versa) (Seinfeld and Pandis 1998). As a result, the influence of the
local emissions is modified by the atmospheric conditions. Over land,
the PBL height exhibits a strong diurnal variability, with lower values
at night. In addition, the mean PBL height varies substantially from day
to day (Seinfeld and Pandis 1998). Besides the vertical transport
(influenced by the PBL), locally emitted air pollutants are also
transported horizontally, where the influence of local sources increases
with decreasing wind speed and vice versa. It is hard to imagine how the
PBL height can be directly related to health except through air
pollution. Similarly, outside of extreme events, wind speed is an
unlikely predictor of health other than through air pollution. As such,
PBL height and wind speed represent attractive options as instruments
for local pollution. However, PBL height and wind speed may vary
seasonally and with temperature and other meteorol ogical parameters. We
believe that within strata of month and deciles of temperature, further
association with predictors of health is unlikely. Hence we looked at
local air pollution variation only within month-byyear strata and within
deciles of temperature (for the full period), and calibrated that
variation with our instruments--that is, we assume short-term predictors
of mortality such as smoking, anger, and the like to be uncorrelated
with PBL height on a day-to-day level, within month-by-year and decile
of temperature. Our analysis took this into account.

A low PBL height and low wind speed are associated with increases
in the concentrations of all locally emitted pollutants. Hence, when
combined into an instrument, it can tell us that local pollution
increases mortality rates (or not), but it will be difficult to identify
which pollutants are responsible for the changed mortality rate.

If a single variable is used as an instrument, that variable can
obtain the estimated causal effect of exposure on the outcome by
regressing the outcome on the instrument, and the instrument on the
exposure of interest. The product of those coefficients is the estimated
causal effect per unit increase in exposure. Because we have four
instrumental variables (PBL and wind speed at lag 0 and lag 1), we
regressed the pollution against the four variables first, and used that
result (the variation in pollution explained by the four instrumental
variables) to generate a single instrumental variable for regression on
the outcome. We have chosen to use these variables as instruments for
[PM.sub.2.5] (particulate matter with aerodynamic diameter [less than or
equal to] 2.5 [micro]m) as the pollutant most strongly associated with
daily deaths. However, this does not demonstrate that the results are
attributable exclusively to particles. We evaluated two alternative air
pollutant exposures as a sensitivity analysis: black carbon (BC), which
represents traffic particles, a large fraction of them locally emitted,
and nitrogen dioxide (N[O.sub.2]), which is mostly from local
combustion.

Data

Mortality Data

We analyzed data from the Boston metropolitan area, which includes
the following counties: Middlesex, Norfolk, and Suffolk. Mortality data
were obtained from the Massachusetts Department of Public Health for the
years 2000-2009. The mortality files provided information on the exact
date of death and the underlying cause of death. We chose all-cause
non-accidental daily mortality [International Classification of
Diseases, 9th Revision (ICD-9) codes 0-799] as our outcome to ensure
sufficient statistical power.

Air Quality Data

[PM.sub.2.5] and BC measurements were conducted at the Harvard
Supersite located on the roof of the Countway Library of the Harvard
Medical School near downtown Boston. Ambient BC was measured
continuously using an aethalometer (Magee Scientific), and [PM.sub.2.5]
was measured continuously using a tapered element oscillating
microbalance (model 1400a; Rupprecht & Pataschnick Co). Daily
averages were computed from the hourly values. We used publicly
available daily data on the height of the PBL obtained from the NOAA
(National Oceanic and Atmospheric Administration) Reanalysis Data (NOAA
2010). Ambient temperature and wind speed were obtained from the Logan
Airport meteorological station.

Analysis

First we orthogonalized our local air pollution exposures to season
and temperature by fitting them to a model with dummy variables for each
month of each year, and for each decile of temperature. We used four
individual variables to derive one single pollution-calibrated
instrumental variable: PBL height and wind speed on the day of death
(lag 0) and PBL height and wind speed on the day before death (lag 1).
To do this, we used a support vector regression (SVM) (Cortes and Vapnik
1995) with a radial kernel to estimate the remaining variation in
[PM.sub.2.5] (or in BC or N[O.sub.2]) that was explained by those four
variables and their products including potential nonlinear dependencies
on the predictors. This approach (support vector kernel regression with
the radial basis kernel) combines our four instruments into one
pollution calibrated instrument, and allows us to compare interquartile
range (IQR) changes in the instruments for local pollution computed
using each of the pollutants ([PM.sub.2.5], BC, or N[O.sub.2]) as an
indicator. The kernel regression also incorporates a ridge penalty to
shrink the coefficients of the multiple terms to avoid overfitting and
collinearity problems. We chose the parameters of the SVM to maximize
10-fold cross-validated [R.sup.2]. We used the svm function in the R
package e1071 (version 3.2; R Project for Statistical Computing). We
checked the [R.sup.2] of the instrument predicting exposure to ensure
our instrument was not too weakly associated with exposure to detect an
effect. Because previous literature has most commonly used the mean of
[PM.sub.2.5] on the day of death and the day preceding death as the
exposure of interest, we used the mean of the instrumental variable on
the day of death and the day preceding the death as our exposure, and
fit a quasi-Poisson regression (allowing for overdispersion) predicting
all-cause mortality. We stratified by each month of each year and by
deciles of temperature, using indicator variables, and estimated the
rate ratio for the instrument.

Boston has lower than average pollution levels for a U.S. city, and
there were no violations of the N[O.sub.2] annual National Ambient Air
Quality (https://www.epa.gov/ criteria-air-pollutants/naaqs-table)
standard of 53 ppb during the study period. There were 19 days which
exceeded the new U.S. EPA [PM.sub.2.5] daily standard of 35
[micro]g/[m.sup.3]. To assure our results apply to low-dose exposures,
we repeated the analyses with the instrument excluding days when
[PM.sub.2.5] exceeded 30 [micro]g/[m.sup.3] to ensure that even with
measurement error the exposure was below the ambient standard. This
excluded 39 days. There are currently no standards for BC.

Granger causality is not a true causal modeling approach, but a
heuristic one that argues that omitted covariates that are correlated
with time-varying exposure and outcome are as likely to be correlated
with tomorrow's exposure as with yesterday's exposure. Hence,
if no association is found between future values of exposure and
outcome, that suggests there is no omitted confounder. Flanders et al.
(2011) give a stronger causal framework using DAGs, and note that the
Granger causality approach assumes that, conditional on exposure and all
confounders, exposure after the outcome should be uncorrelated with the
outcome. However, exposure after the outcome and exposure before the
outcome are both associated with the confounders, as illustrated in the
DAG in Figure 2. Therefore, in the presence of omitted confounders an
association may be expected with the future exposure. Hence, if we fit a
model with the past exposure and the future exposure and find an
association only with the past exposure, that would argue against such
omitted confounders, and vice versa. We tested this approach by
rerunning our instrumental variable model with the mean of the
instrument (lags 0 and 1) and the mean value of the instrument on the
second and third days after death. We left 1 day between the exposure
before the event and the exposure after the event to produce more stable
estimates for each association, given the serial correlation in
pollution.

We also conducted a sensitivity analysis to test our assumption
that we had a valid instrument. Looking at Figure 1 again, we see that
the instrumental variable (Z) is associated only with the outcome
through the exposure (A) (the assumption for instrumental variables).
That is, the exposure can be viewed as a mediator of the association of
the instrumental variable with the outcome. Then if we control for A,
there should be no association with the instrument any longer (no direct
effect) by that assumption. If, in contrast, an association remains,
then there is another path from Z to the outcome, through some
confounder. We tested this by fitting a model with both our instrument
and the original exposure variable ([PM.sub.2.5]).

To put our results in context, we performed a quantitative health
impact assessment. Specifically, we estimated the reduction in deaths
during the 10 years of study for an IQR reduction in our instrumental
variable (after ensuring that such a reduction from the mean would
result in an exposure above zero). This was estimated as

change in deaths = RR -1/RR Total Deaths

where RR is the rate ratio for the change in exposure, exp(b1 x
IQR) where b1 is the coefficient of the instrumental variable, and IQR
is its interquartile range. This approach is standard in risk assessment
(Fann et al. 2011; GBD 2013 Risk Factors Collaborators et al. 2015; U.S.
EPA 1999). We computed the total deaths during follow-up (204,386) from
our data.

Results

Table 1 shows descriptive statistics for the variables in our
study. Air pollution concentrations were low, and almost always well
below the current U.S. EPA standards (results not shown). Table 2 shows
the correlations among the covariates. The correlation between
[PM.sub.2.5] and BC was 0.65, between [PM.sub.2.5] and N[O.sub.2] was
0.45, and between BC and N[O.sub.2] was 0.57. The correlation between
air pollution and the candidate instruments were modest. For example,
for [PM.sub.2.5], the correlation with PBL height was -0.35, and with
wind speed was -0.28.

Instrumental Variable Model

If a model predicting a variable is over fit (e.g., uses too many
degrees of freedom), then one would expect the predicted [R.sup.2] on
left-out monitors to be noticeably smaller than the model [R.sup.2] in
the training data set. The cross-validated [R.sup.2] of the instrumental
variable predicting [PM.sub.2.5] was 0.180, little changed from the
[R.sup.2] in the training data (0.189). Although low, this is consistent
with the fact that most of the [PM.sub.2.5] in Boston is transported
rather than locally emitted, and with PM having other important sources
of variation besides PBL and wind speed (Masri et al. 2015). Overfitting
was avoided because the tuning parameters of the model calibrating the
instrument to [PM.sub.2.5] were chosen by cross-validation, and because
the SVM uses a ridge penalty, where a penalty term is added to the cost
function proportional to the sum of the square of the regression
coefficients. This penalty constrains the coefficients from varying
wildly, or growing too large.

As expected, PBL height and wind speed were better predictors of BC
(a large fraction of which is locally emitted) than of [PM.sub.2.5]. The
cross-validated [R.sup.2] of the SVM model for BC was 0.36, versus 0.37
without cross-validation. Similarly, the SVM model for N[O.sub.2] had a
cross-validated [R.sup.2] of 0.39, versus 0.40 without cross-validation.

Mortality Model

An IQR change in the instrument for local [PM.sub.2.5] was
associated with a 0.90% increase in daily deaths [95% confidence
interval (CI): 0.25, 1.56], whereas an IQR change in the instrument for
BC was associated with a 0.90% increase in daily deaths (95% CI: 0.08,
1.73). For N[O.sub.2], an IQR increase in the instrument was associated
with a 0.62% increase in daily deaths (95% CI: -0.12, 1.64). We compared
IQR changes for the instrumental variables to have some basis for
comparing effects between the models for [PM.sub.2.5], BC, and
N[O.sub.2]. When the mortality analysis was restricted to days when
[PM.sub.2.5] was < 30 [micro]g/[m.sup.3] (which excluded 39 days), we
found a 0.84% increase in daily deaths for the same increase in the
instrument (95% CI: 0.19, 1.50).

When we used the Granger causality approach, the estimated effect
of an IQR change in the instrument for [PM.sub.2.5] remained the same
(0.90%; 95% CI: 0.25, 1.96), whereas the forward lagged instrument was
not associated with mortality (0.18%; 95% CI: -0.45, 0.81), suggesting
no omitted confounders. Although the power for a Granger causality test
may not be strong, the much smaller effect size as well as lack of
significance both indicate a lack of confounding.

Finally, when we added the mean of [PM.sub.2.5] on lags 0 and 1 to
the model in addition to the instrumental variable, the instrumental
variable was far from significant (p > 0.29) while the [PM.sub.2.5]
variable was significant. This indicates that there was no path from
instrument to the outcome except through [PM.sub.2.5], and hence that
the instrumental variable assumption was valid.

Discussion

Using a framework based on potential outcomes, we have estimated
the causal effect of an IQR increase in local air pollution on daily
deaths in Boston. The increase in deaths for an IQR increase in the
instrument for exposure was about 0.90% using either particle measure to
calibrate the instrument; for N[O.sub.2] it was lower (0.62%) with
confidence intervals that crossed zero. Using the approach of Granger
causality, we saw no change in the estimated effect of our instrument
when controlling for exposure on future days and the association with
future exposure was close to zero and far from significant. Further, the
association persisted when restricted to days well below the recently
tightened U.S. EPA 24-hr standard for [PM.sub.2.5] (35
[micro]g/[m.sup.3]), and in a city that never violated the hourly
N[O.sub.2] National Ambient Air Quality standard during the study
period. Hence, these effects are evident at levels below currently
permissible limits.

A key advantage of the instrumental variable approach is that it
provides protection against unmeasured confounders. We have approached
this in three ways. First, we have shown that if we have a valid
instrument, then the association will be causal even in the presence of
unmeasured confounders. We focused on the variation in local pollution
within deciles of temperature and also stratified on each month of each
year. We then chose as instruments variables (PBL height and wind speed)
we believed, based on external knowledge, are unlikely to be associated
with mortality except through air pollution. Second, we have confirmed
that values of the instrument following the day of death are not
significantly associated (p = 0.57) with daily deaths, and that control
for them did not change the estimated effect of the instrument. This
assures that omitted confounders with the same broad temporal
variability are not confounding our instrument. And third, we have
tested the instrument assumption (that the association of the instrument
is only through air pollution) by controlling for air pollution, and
showing that no significant association with the instrument remained (p
> 0.29). We believe that this makes a strong case for a causal
effect.

Support for this causal interpretation also comes from an extensive
toxicological and human exposure literature on some of these local
pollutants. For example, Furuyama et al. (2006) found increased
oxidative stress in endothelial cells exposed to diesel exhaust, and in
humans Rossner et al. (2007) reported increased levels of F-2
isoprostane and 8-OHdG (8-hydroxy-2r-deoxyguanosine) in bus drivers
compared with controls. The human study contrasted urinary 8-OHdG in 50
bus drivers and 50 controls measured in three successive seasons in
Prague. In logistic regression analysis, [PM.sub.2.5], but not volatile
organic compound or polycyclic aromatic hydrocarbon exposure, was
associated with 8-OHdG. Romieu et al. (2008) measured malondialdehyde in
exhaled breath condensate at 480 visits in a panel of 108 children with
asthma seen every 2 weeks, and found it was positively associated with
[PM.sub.2.5] at the nearest monitoring station within 5 km of their home
and school.

Increased atherosclerosis has also been reported in animals with
long-term exposure to particles, much of which was from traffic (Sun et
al. 2005, 2008). Another study (Soares et al. 2009) placed hyperlipemic
mice in two exposure chambers 20 m from a road. One chamber was filtered
to remove particles and the other was not. After 120 days of exposure
they documented increased oxidation of lowdensity lipoprotein, increased
thickness of the arterial wall, and greater plaque growth and
instability (Soares et al. 2009). Along with the increased oxidative
stress, atherosclerosis, and plaque instability, increased thrombosis
has also been associated with local pollution. Nemmar et al. (2002,
2003) found that both diesel and ultrafine particles were associated
with increased thrombosis in an animal model, and Carlsten et al. (2007,
2008) found that controlled exposure to diesel exhaust increased
coagulation markers and thrombosis in human volunteers. Ischemia has
likewise been produced experimentally by diesel exposure in a
double-blind randomized crossover exposure of 20 people with previous
myocardial infarction to 1 hr of dilute diesel exhaust or filtered air
(Mills et al. 2007).

An intervention trial in Beijing had 15 young adults (median age,
28 years) walk the streets for 2 hr twice, once wearing a
particle-filtering mask, and once without a mask. Blood pressure was
measured continuously during the two 2-hr walks and was 7 mmHg lower
when wearing the mask (Langrish et al. 2009). These results, combined
with the instrumental variable approach and Granger causality model,
support a causal interpretation.

The weaker association of the instrumental variables when
calibrated to N[O.sub.2] than to particles suggests that local particles
may be more important in this relationship, but no definite conclusions
can be drawn.

To put this result in context, the mean [PM.sub.2.5], N[O.sub.2],
and BC (9.8 [micro]g/[m.sup.3], 18.4 ppb, and 0.7 [micro]g/[m.sup.3])
were all greater than their IQRs (6.32 [micro]g/[m.sup.3], 8.4 ppb, and
0.50 [micro]g/[m.sup.3], respectively), indicating that IQR changes in
the pollutant concentrations would result in levels above zero, and
hence are plausible. Computing the attributable risk for an IQR change
in exposure to the instrument, we estimated that local air pollution was
responsible for 1,826 deaths in the Boston metropolitan area during the
study period. This is a substantial public health burden.

Local air pollution in Boston has multiple sources, including
traffic, combustion of fuel oil and residual oil for heating, and wood
burning (Masri et al. 2015). Traffic pollution has fallen because of
reduced U.S. EPA emission standards on vehicles, low-sulfur diesel oil
requirements, the retrofit of particle filters onto buses, and the
introduction of compressed natural gas buses for part of the fleet
(Masri et al. 2015; U.S. EPA 2012). Continuing retirement of older
vehicles will likely continue this trend. Wood burning, on the other
hand has increased and now accounts for 19% of particles in Boston
(Masri et al. 2015), and though the U.S. EPA has proposed new emission
standards for future stoves and furnaces, there is no retrofit
requirement. Heating oil, while similar to diesel oil, is still allowed
much higher sulfur content. Hence, there are opportunities for local
action to reduce this public health burden.

There are several limitations to our study. First, we have assumed
we have a valid instrument. Although we have good evidence that this is
the case, one can never guarantee it. It is possible that behavior is
modified on low-PBL or low-wind speed days in a way that affects
mortality risk. A second limitation is that we have provided our proof
that an instrumental variable protects against unmeasured confounding in
the context of a log-linear model between mortality and air pollution,
and assume that model is correct. This is the traditional approach for
daily death counts, but we cannot be sure it is correct. In addition,
all-cause mortality includes some causes of death unlikely to be
associated with air pollution. This decreases power in our analysis, but
still leaves us with a valid estimate of the impact on all deaths. The
air pollutants, PBL, and wind speed were measured at only one location,
which may introduce some error into the instrumental variable, which, if
the instrument assumption is valid, should result in an underestimate of
risk. Power is always an issue, and the power for a Poisson regression
depends on the total number of events. In our case, there were 204,386
deaths during the study period, which indicates good power for our
hypothesis tests.

In summary, we have used causal methods to estimate the acute
effect of local air pollution on daily deaths, and found that
concentrations below current limits are associated with important
increases in daily deaths. If, when stratified by month and temperature,
our instrument is independent of other causes of mortality, this
association is causal, an interpretation supported by toxicological
studies.

Schwartz J. 2004a. Is the association of airborne particles with
daily deaths confounded by gaseous air pollutants? An approach to
control by matching. Environ Health Perspect 112:557-561, doi: 10.1289/
ehp.6431.

This research was supported in part by National Institute of
Environmental Health Sciences/National Institutes of Health grant
ES-000002, and by U.S. Environmental Protection Agency (EPA) grant RD
83479801 to J.S. and P.K.

The contents of this publication are solely the responsibility of
the grantee and do not necessarily represent the official views of the
U.S. EPA.

The authors declare they have no actual or potential competing
financial interests.

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Caption: Figure 1. Directed acyclic graph illustrating an
instrumental variable Z. The association between Zand Yis not confounded
by C. By calibrating the instrument to A, estimates of causal effects of
increases in A can be obtained.

Caption: Figure 2. Directed acyclic graph for the Granger causality
model. Confounder U2 is measured and controlled, but confounder U1 is
not. [POL.sub.b] is pollution before the outcome (O), and [POL.sub.a] is
pollution after the outcome. If U1 is not controlled, there is a
backdoor path from O to [POL.sub.a], and an association would be
expected. Hence, failure to find an association is evidence of a lack of
confounding (i.e., no U1).